Base field 5.5.160801.1
Generator \(w\), with minimal polynomial \(x^{5} - x^{4} - 5x^{3} + 4x^{2} + 3x - 1\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2, 2]$ |
| Level: | $[9, 3, -w^{4} + w^{3} + 5w^{2} - 3w - 2]$ |
| Dimension: | $7$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $13$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{7} - 13x^{5} - 3x^{4} + 35x^{3} - 4x^{2} - 13x - 1\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, w^{4} - w^{3} - 5w^{2} + 3w + 3]$ | $\phantom{-}e$ |
| 9 | $[9, 3, -w^{4} + 5w^{2} - 3]$ | $-\frac{2}{3}e^{5} + \frac{1}{3}e^{4} + \frac{20}{3}e^{3} + \frac{4}{3}e^{2} - \frac{26}{3}e - \frac{7}{3}$ |
| 9 | $[9, 3, -w^{4} + w^{3} + 5w^{2} - 3w - 2]$ | $\phantom{-}1$ |
| 13 | $[13, 13, -w^{4} + w^{3} + 4w^{2} - 3w - 1]$ | $-\frac{4}{3}e^{6} + \frac{1}{3}e^{5} + 16e^{4} + 2e^{3} - \frac{110}{3}e^{2} + 5e + \frac{22}{3}$ |
| 17 | $[17, 17, w^{4} - w^{3} - 5w^{2} + 3w + 1]$ | $-\frac{2}{3}e^{6} + \frac{22}{3}e^{4} + \frac{11}{3}e^{3} - 12e^{2} - \frac{8}{3}e + \frac{10}{3}$ |
| 19 | $[19, 19, -w^{3} + w^{2} + 4w - 2]$ | $-\frac{1}{3}e^{6} + \frac{1}{3}e^{5} + 4e^{4} - 2e^{3} - \frac{29}{3}e^{2} + 3e - \frac{2}{3}$ |
| 23 | $[23, 23, -w^{2} + 3]$ | $\phantom{-}\frac{1}{3}e^{6} + \frac{1}{3}e^{5} - \frac{16}{3}e^{4} - \frac{8}{3}e^{3} + \frac{52}{3}e^{2} - \frac{19}{3}e - 6$ |
| 31 | $[31, 31, w^{3} - 4w + 2]$ | $\phantom{-}\frac{2}{3}e^{6} - \frac{31}{3}e^{4} + \frac{4}{3}e^{3} + 36e^{2} - \frac{58}{3}e - \frac{31}{3}$ |
| 32 | $[32, 2, 2]$ | $\phantom{-}\frac{1}{3}e^{6} - \frac{14}{3}e^{4} - \frac{4}{3}e^{3} + 14e^{2} + \frac{10}{3}e - \frac{14}{3}$ |
| 37 | $[37, 37, w^{3} - 3w - 1]$ | $-\frac{1}{3}e^{6} + e^{5} + \frac{8}{3}e^{4} - \frac{23}{3}e^{3} - 3e^{2} + \frac{32}{3}e + \frac{8}{3}$ |
| 53 | $[53, 53, -2w^{4} + w^{3} + 9w^{2} - 3w - 2]$ | $-\frac{5}{3}e^{6} - \frac{2}{3}e^{5} + \frac{68}{3}e^{4} + \frac{28}{3}e^{3} - \frac{182}{3}e^{2} + \frac{32}{3}e + 14$ |
| 59 | $[59, 59, -w^{4} + 5w^{2} + w - 4]$ | $-\frac{4}{3}e^{6} - \frac{4}{3}e^{5} + \frac{52}{3}e^{4} + \frac{53}{3}e^{3} - \frac{112}{3}e^{2} - \frac{29}{3}e + 4$ |
| 61 | $[61, 61, -w^{4} + w^{3} + 5w^{2} - 4w]$ | $\phantom{-}e^{6} - 12e^{4} - 4e^{3} + 25e^{2} - 4$ |
| 67 | $[67, 67, -w^{4} + 6w^{2} + 2w - 4]$ | $-2e^{6} - e^{5} + 24e^{4} + 19e^{3} - 48e^{2} - 13e + 8$ |
| 71 | $[71, 71, 2w^{4} - w^{3} - 9w^{2} + 4w + 5]$ | $-\frac{1}{3}e^{6} - e^{5} + \frac{17}{3}e^{4} + \frac{25}{3}e^{3} - 15e^{2} + \frac{11}{3}e - \frac{1}{3}$ |
| 79 | $[79, 79, 2w^{4} - w^{3} - 10w^{2} + 2w + 7]$ | $\phantom{-}e^{6} + \frac{1}{3}e^{5} - \frac{38}{3}e^{4} - \frac{22}{3}e^{3} + \frac{91}{3}e^{2} + \frac{7}{3}e - \frac{19}{3}$ |
| 83 | $[83, 83, -w^{4} + 2w^{3} + 5w^{2} - 7w - 2]$ | $\phantom{-}\frac{5}{3}e^{6} - \frac{61}{3}e^{4} - \frac{23}{3}e^{3} + 47e^{2} + \frac{11}{3}e - \frac{25}{3}$ |
| 83 | $[83, 83, -w^{4} + w^{3} + 4w^{2} - 3w + 3]$ | $-\frac{1}{3}e^{6} + \frac{5}{3}e^{5} + \frac{10}{3}e^{4} - \frac{52}{3}e^{3} - \frac{31}{3}e^{2} + \frac{112}{3}e + 2$ |
| 83 | $[83, 83, w^{4} - w^{3} - 5w^{2} + 4w - 1]$ | $-e^{6} + \frac{5}{3}e^{5} + \frac{35}{3}e^{4} - \frac{38}{3}e^{3} - \frac{103}{3}e^{2} + \frac{59}{3}e + \frac{43}{3}$ |
| 83 | $[83, 83, -w^{4} + w^{3} + 4w^{2} - 4w - 2]$ | $\phantom{-}2e^{6} + \frac{1}{3}e^{5} - \frac{80}{3}e^{4} - \frac{22}{3}e^{3} + \frac{214}{3}e^{2} - \frac{47}{3}e - \frac{46}{3}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $9$ | $[9, 3, -w^{4} + w^{3} + 5w^{2} - 3w - 2]$ | $-1$ |